What is a Beam Width, Beam Size, and a Beam Waist?

Posted on 2007-07-11. Permanent link: http://www.rp-photonics.com/spotlight_2007_07_11.html

Author: Dr. Rüdiger Paschotta, RP Photonics Consulting GmbH

Ref.: encyclopedia articles on beam radius and beam divergence

Scientists as well as engineers are expected to communicate clearly, minimizing the risk of misunderstanding. Surprisingly, certain wordings, which constantly cause confusion, are very abundant in the scientific and technical literature. Some of those are related to the transverse extension of laser beams:

• Terms like "beam size", "waist size", "beam width" and the like are suitable only for qualitative statements like "The beam size sharply increases as the resonator length approaches the stability limit". But nobody knows for sure whether some "size" or "width" refers to beam diameter or beam radius. The former meaning may seem more plausible, but the latter is frequently meant. So such imprecise wording easily introduces an error of a factor of 2 in dimensions, and a factor of 4 in the beam area.
• Some researchers should at least once have a look at a slim lady, search for her waist, and remember that the beam waist of some laser beam is essentially the same: the part where the transverse extension is smallest. It is certainly not a diameter or radius, measured just anywhere along the beam.
• A similar analogy occurs when quantifying the diameter either of a laser beam or a lady. In the latter case, it should be made clear whether one measures only the extent of dense matter or also includes the aura in some way. The latter is obviously more difficult, but perhaps also more relevant. For laser beams, one may measure e.g. up to points where the intensity decreases to 1/e² or to 50% of the maximum intensity, or one may use some variance-type integral. The results can strongly depend on the used definition.
• Essentially the same issues arise in the context of quantifying a beam divergence. While manufacturers of laser diodes seem to prefer FWHM angles, scientists are more likely to use values based on half-angles measured at 1/e² intensity.

So my suggestion is to avoid a lot of confusion by making precise statements on all quantitative aspects of laser beams. Even in scientific papers, one all too often finds oneself in a situation where one has to construct sophisticated theories concerning what the author might have meant.